def update_mobject(self, alpha):
new_tex = self.tex_list[np.ceil(alpha * len(self.tex_list)) - 1]
if new_tex != self.curr_tex:
self.curr_tex = new_tex
self.mobject = TexMobject(new_tex).shift(self.start_center)
if not all(self.start_center == self.end_center):
self.mobject.center().shift(
(1 - alpha) * self.start_center + alpha * self.end_center
)
def generate_sea_of_zeros(self):
zero = TexMobject("0")
self.sea_of_zeros = []
for n in range(self.nrows):
for a in range((self.nrows - n) / 2 + 1):
for k in (n + a + 1, -a - 1):
self.coords.append((n, k))
mob = zero.copy()
mob.shift(self.coords_to_center(n, k))
self.coords_to_mobs[n][k] = mob
self.add(mob)
return self
def get_coordinate_labels(self, *numbers):
# TODO: Should merge this with the code from NumberPlane.get_coordinate_labels
result = VGroup()
if len(numbers) == 0:
numbers = list(range(-int(self.x_radius), int(self.x_radius) + 1))
numbers += [
complex(0, y) for y in range(-int(self.y_radius),
int(self.y_radius) + 1)
]
for number in numbers:
if number == complex(0, 0):
continue
point = self.number_to_point(number)
num_str = str(number).replace("j", "i")
if num_str.startswith("0"):
num_str = "0"
elif num_str in ["1i", "-1i"]:
num_str = num_str.replace("1", "")
num_mob = TexMobject(num_str)
num_mob.add_background_rectangle()
num_mob.set_height(self.written_coordinate_height)
num_mob.next_to(point, DOWN + LEFT, SMALL_BUFF)
result.add(num_mob)
self.coordinate_labels = result
return result
def __init__(self, mobject, direction=DOWN, **kwargs):
digest_config(self, kwargs, locals())
angle = -np.arctan2(*direction[:2]) + np.pi
mobject.rotate(-angle, about_point=ORIGIN)
left = mobject.get_corner(DOWN + LEFT)
right = mobject.get_corner(DOWN + RIGHT)
target_width = right[0] - left[0]
# Adding int(target_width) qquads gives approximately the right width
num_quads = np.clip(int(self.width_multiplier * target_width),
self.min_num_quads, self.max_num_quads)
tex_string = "\\underbrace{%s}" % (num_quads * "\\qquad")
TexMobject.__init__(self, tex_string, **kwargs)
self.tip_point_index = np.argmin(self.get_all_points()[:, 1])
self.stretch_to_fit_width(target_width)
self.shift(left - self.get_corner(UP + LEFT) + self.buff * DOWN)
for mob in mobject, self:
mob.rotate(angle, about_point=ORIGIN)
def count_mobjects(self,
mobjects,
mode="highlight",
color="red",
display_numbers=True,
num_offset=DEFAULT_COUNT_NUM_OFFSET,
run_time=DEFAULT_COUNT_RUN_TIME):
"""
Note, leaves final number mobject as "number" attribute
mode can be "highlight", "show_creation" or "show", otherwise
a warning is given and nothing is animating during the count
"""
if len(mobjects) > 50: #TODO
raise Exception("I don't know if you should be counting \
too many mobjects...")
if len(mobjects) == 0:
raise Exception("Counting mobject list of length 0")
if mode not in ["highlight", "show_creation", "show"]:
raise Warning("Unknown mode")
frame_time = run_time / len(mobjects)
if mode == "highlight":
self.add(*mobjects)
for mob, num in zip(mobjects, it.count(1)):
if display_numbers:
num_mob = TexMobject(str(num))
num_mob.center().shift(num_offset)
self.add(num_mob)
if mode == "highlight":
original_color = mob.color
mob.set_color(color)
self.wait(frame_time)
mob.set_color(original_color)
if mode == "show_creation":
self.play(ShowCreation(mob, run_time=frame_time))
if mode == "show":
self.add(mob)
self.wait(frame_time)
if display_numbers:
self.remove(num_mob)
if display_numbers:
self.add(num_mob)
self.number = num_mob
return self
class FlipThroughSymbols(Animation):
CONFIG = {
"start_center": ORIGIN,
"end_center": ORIGIN,
}
def __init__(self, tex_list, **kwargs):
mobject = TexMobject(self.curr_tex).shift(start_center)
Animation.__init__(self, mobject, **kwargs)
def update_mobject(self, alpha):
new_tex = self.tex_list[np.ceil(alpha * len(self.tex_list)) - 1]
if new_tex != self.curr_tex:
self.curr_tex = new_tex
self.mobject = TexMobject(new_tex).shift(self.start_center)
if not all(self.start_center == self.end_center):
self.mobject.center().shift(
(1 - alpha) * self.start_center + alpha * self.end_center
)
def count_regions(self,
regions,
mode="one_at_a_time",
num_offset=DEFAULT_COUNT_NUM_OFFSET,
run_time=DEFAULT_COUNT_RUN_TIME,
**unused_kwargsn):
if mode not in ["one_at_a_time", "show_all"]:
raise Warning("Unknown mode")
frame_time = run_time / (len(regions))
for region, count in zip(regions, it.count(1)):
num_mob = TexMobject(str(count))
num_mob.center().shift(num_offset)
self.add(num_mob)
self.set_color_region(region)
self.wait(frame_time)
if mode == "one_at_a_time":
self.reset_background()
self.remove(num_mob)
self.add(num_mob)
self.number = num_mob
return self
def get_result_matrix(self, left, right):
(m, k), n = left.shape, right.shape[1]
mob_matrix = np.array([VGroup()]).repeat(m * n).reshape((m, n))
for a in range(m):
for b in range(n):
template = "(%s)(%s)" if self.use_parens else "%s%s"
parts = [
prefix + template % (left[a][c], right[c][b])
for c in range(k) for prefix in ["" if c == 0 else "+"]
]
mob_matrix[a][b] = TexMobject(parts, next_to_buff=0.1)
return Matrix(mob_matrix)
def add_brackets(self):
bracket_pair = TexMobject("\\big[ \\big]")
bracket_pair.scale(2)
bracket_pair.stretch_to_fit_height(self.get_height() + 0.5)
l_bracket, r_bracket = bracket_pair.split()
l_bracket.next_to(self, LEFT)
r_bracket.next_to(self, RIGHT)
self.add(l_bracket, r_bracket)
self.brackets = VGroup(l_bracket, r_bracket)
return self
def generate_points(self):
start_angle = np.pi / 2 + self.arc_angle / 2
end_angle = np.pi / 2 - self.arc_angle / 2
self.add(Arc(start_angle=start_angle, angle=-self.arc_angle))
tick_angle_range = np.linspace(start_angle, end_angle, self.num_ticks)
for index, angle in enumerate(tick_angle_range):
vect = rotate_vector(RIGHT, angle)
tick = Line((1 - self.tick_length) * vect, vect)
label = TexMobject(str(10 * index))
label.set_height(self.tick_length)
label.shift((1 + self.tick_length) * vect)
self.add(tick, label)
needle = Polygon(LEFT,
UP,
RIGHT,
stroke_width=0,
fill_opacity=1,
fill_color=self.needle_color)
needle.stretch_to_fit_width(self.needle_width)
needle.stretch_to_fit_height(self.needle_height)
needle.rotate(start_angle - np.pi / 2, about_point=ORIGIN)
self.add(needle)
self.needle = needle
self.center_offset = self.get_center()
def add_axes(self):
x_axis = Line(self.tick_width * LEFT / 2, self.width * RIGHT)
y_axis = Line(MED_LARGE_BUFF * DOWN, self.height * UP)
ticks = VGroup()
heights = np.linspace(0, self.height, self.n_ticks + 1)
values = np.linspace(0, self.max_value, self.n_ticks + 1)
for y, value in zip(heights, values):
tick = Line(LEFT, RIGHT)
tick.set_width(self.tick_width)
tick.move_to(y * UP)
ticks.add(tick)
y_axis.add(ticks)
self.add(x_axis, y_axis)
self.x_axis, self.y_axis = x_axis, y_axis
if self.label_y_axis:
labels = VGroup()
for tick, value in zip(ticks, values):
label = TexMobject(str(np.round(value, 2)))
label.set_height(self.y_axis_label_height)
label.next_to(tick, LEFT, SMALL_BUFF)
labels.add(label)
self.y_axis_labels = labels
self.add(labels)
def get_number_mob(self, num):
result = VGroup()
place = 0
max_place = self.max_place
while place < max_place:
digit = TexMobject(str(self.get_place_num(num, place)))
if place >= len(self.digit_place_colors):
self.digit_place_colors += self.digit_place_colors
digit.set_color(self.digit_place_colors[place])
digit.scale(self.num_scale_factor)
digit.next_to(result, LEFT, buff=SMALL_BUFF, aligned_edge=DOWN)
result.add(digit)
place += 1
return result
def get_subdivision_braces_and_labels(self,
parts,
labels,
direction,
buff=SMALL_BUFF,
min_num_quads=1):
label_mobs = VGroup()
braces = VGroup()
for label, part in zip(labels, parts):
brace = Brace(part,
direction,
min_num_quads=min_num_quads,
buff=buff)
if isinstance(label, Mobject):
label_mob = label
else:
label_mob = TexMobject(label)
label_mob.scale(self.default_label_scale_val)
label_mob.next_to(brace, direction, buff)
braces.add(brace)
label_mobs.add(label_mob)
parts.braces = braces
parts.labels = label_mobs
parts.label_kwargs = {
"labels": label_mobs.copy(),
"direction": direction,
"buff": buff,
}
return VGroup(parts.braces, parts.labels)
def add_T_label(self,
x_val,
side=RIGHT,
label=None,
color=WHITE,
animated=False,
**kwargs):
triangle = RegularPolygon(n=3, start_angle=np.pi / 2)
triangle.set_height(MED_SMALL_BUFF)
triangle.move_to(self.coords_to_point(x_val, 0), UP)
triangle.set_fill(color, 1)
triangle.set_stroke(width=0)
if label == None:
T_label = TexMobject(self.variable_point_label, fill_color=color)
else:
T_label = TexMobject(label, fill_color=color)
T_label.next_to(triangle, DOWN)
v_line = self.get_vertical_line_to_graph(x_val,
self.v_graph,
color=YELLOW)
if animated:
self.play(DrawBorderThenFill(triangle), ShowCreation(v_line),
Write(T_label, run_time=1), **kwargs)
if np.all(side == LEFT):
self.left_T_label_group = VGroup(T_label, triangle)
self.left_v_line = v_line
self.add(self.left_T_label_group, self.left_v_line)
elif np.all(side == RIGHT):
self.right_T_label_group = VGroup(T_label, triangle)
self.right_v_line = v_line
self.add(self.right_T_label_group, self.right_v_line)
def get_mobs_from_terms(self, start_terms, end_terms):
"""
Need to ensure that all image mobjects for a tex expression
stemming from the same string are point-for-point copies of one
and other. This makes transitions much smoother, and not look
like point-clouds.
"""
num_start_terms = len(start_terms)
all_mobs = np.array(
TexMobject(start_terms).split() +
TexMobject(end_terms).split()
)
all_terms = np.array(start_terms + end_terms)
for term in set(all_terms):
matches = all_terms == term
if sum(matches) > 1:
base_mob = all_mobs[list(all_terms).index(term)]
all_mobs[matches] = [
base_mob.copy().replace(target_mob)
for target_mob in all_mobs[matches]
]
return all_mobs[:num_start_terms], all_mobs[num_start_terms:]
def get_axis_labels(self, x_label="x", y_label="y"):
x_axis, y_axis = self.get_axes().split()
quads = [
(x_axis, x_label, UP, RIGHT),
(y_axis, y_label, RIGHT, UP),
]
labels = VGroup()
for axis, tex, vect, edge in quads:
label = TexMobject(tex)
label.add_background_rectangle()
label.next_to(axis, vect)
label.to_edge(edge)
labels.add(label)
self.axis_labels = labels
return labels
def setup(self):
self.dots = VGroup()
self.number = 0
self.max_place = 0
self.number_mob = VGroup(TexMobject(str(self.number)))
self.number_mob.scale(self.num_scale_factor)
self.number_mob.shift(self.num_start_location)
self.dot_templates = []
self.dot_template_iterators = []
self.curr_configurations = []
self.arrows = VGroup()
self.add(self.number_mob)
def get_coordinate_labels(self, x_vals=None, y_vals=None):
coordinate_labels = VGroup()
if x_vals is None:
x_vals = list(range(-int(self.x_radius), int(self.x_radius) + 1))
if y_vals is None:
y_vals = list(range(-int(self.y_radius), int(self.y_radius) + 1))
for index, vals in enumerate([x_vals, y_vals]):
num_pair = [0, 0]
for val in vals:
if val == 0:
continue
num_pair[index] = val
point = self.coords_to_point(*num_pair)
num = TexMobject(str(val))
num.add_background_rectangle()
num.set_height(self.written_coordinate_height)
num.next_to(point, DOWN + LEFT, buff=SMALL_BUFF)
coordinate_labels.add(num)
self.coordinate_labels = coordinate_labels
return coordinate_labels
def generate_n_choose_k_mobs(self):
self.coords_to_n_choose_k = {}
for n, k in self.coords:
nck_mob = TexMobject(r"{%d \choose %d}" % (n, k))
scale_factor = min(
1,
self.portion_to_fill * self.cell_height / nck_mob.get_height(),
self.portion_to_fill * self.cell_width / nck_mob.get_width(),
)
center = self.coords_to_mobs[n][k].get_center()
nck_mob.center().scale(scale_factor).shift(center)
if n not in self.coords_to_n_choose_k:
self.coords_to_n_choose_k[n] = {}
self.coords_to_n_choose_k[n][k] = nck_mob
return self
def get_graph_label(
self,
graph,
label="f(x)",
x_val=None,
direction=RIGHT,
buff=MED_SMALL_BUFF,
color=None,
):
label = TexMobject(label)
color = color or graph.get_color()
label.set_color(color)
if x_val is None:
# Search from right to left
for x in np.linspace(self.x_max, self.x_min, 100):
point = self.input_to_graph_point(x, graph)
if point[1] < FRAME_Y_RADIUS:
break
x_val = x
label.next_to(self.input_to_graph_point(x_val, graph),
direction,
buff=buff)
label.shift_onto_screen()
return label
def add_bars(self, values):
buff = float(self.width) / (2 * len(values) + 1)
bars = VGroup()
for i, value in enumerate(values):
bar = Rectangle(
height=(value / self.max_value) * self.height,
width=buff,
stroke_width=self.bar_stroke_width,
fill_opacity=self.bar_fill_opacity,
)
bar.move_to((2 * i + 1) * buff * RIGHT, DOWN + LEFT)
bars.add(bar)
bars.set_color_by_gradient(*self.bar_colors)
bar_labels = VGroup()
for bar, name in zip(bars, self.bar_names):
label = TexMobject(str(name))
label.scale(self.bar_label_scale_val)
label.next_to(bar, DOWN, SMALL_BUFF)
bar_labels.add(label)
self.add(bars, bar_labels)
self.bars = bars
self.bar_labels = bar_labels
def get_vector_label(self,
vector,
label,
at_tip=False,
direction="left",
rotate=False,
color=None,
label_scale_factor=VECTOR_LABEL_SCALE_FACTOR):
if not isinstance(label, TexMobject):
if len(label) == 1:
label = "\\vec{\\textbf{%s}}" % label
label = TexMobject(label)
if color is None:
color = vector.get_color()
label.set_color(color)
label.scale(label_scale_factor)
label.add_background_rectangle()
if at_tip:
vect = vector.get_vector()
vect /= get_norm(vect)
label.next_to(vector.get_end(), vect, buff=SMALL_BUFF)
else:
angle = vector.get_angle()
if not rotate:
label.rotate(-angle, about_point=ORIGIN)
if direction is "left":
label.shift(-label.get_bottom() + 0.1 * UP)
else:
label.shift(-label.get_top() + 0.1 * DOWN)
label.rotate(angle, about_point=ORIGIN)
label.shift((vector.get_end() - vector.get_start()) / 2)
return label
def get_secant_slope_group(
self,
x,
graph,
dx=None,
dx_line_color=None,
df_line_color=None,
dx_label=None,
df_label=None,
include_secant_line=True,
secant_line_color=None,
secant_line_length=10,
):
"""
Resulting group is of the form VGroup(
dx_line,
df_line,
dx_label, (if applicable)
df_label, (if applicable)
secant_line, (if applicable)
)
with attributes of those names.
"""
kwargs = locals()
kwargs.pop("self")
group = VGroup()
group.kwargs = kwargs
dx = dx or float(self.x_max - self.x_min) / 10
dx_line_color = dx_line_color or self.default_input_color
df_line_color = df_line_color or graph.get_color()
p1 = self.input_to_graph_point(x, graph)
p2 = self.input_to_graph_point(x + dx, graph)
interim_point = p2[0] * RIGHT + p1[1] * UP
group.dx_line = Line(p1, interim_point, color=dx_line_color)
group.df_line = Line(interim_point, p2, color=df_line_color)
group.add(group.dx_line, group.df_line)
labels = VGroup()
if dx_label is not None:
group.dx_label = TexMobject(dx_label)
labels.add(group.dx_label)
group.add(group.dx_label)
if df_label is not None:
group.df_label = TexMobject(df_label)
labels.add(group.df_label)
group.add(group.df_label)
if len(labels) > 0:
max_width = 0.8 * group.dx_line.get_width()
max_height = 0.8 * group.df_line.get_height()
if labels.get_width() > max_width:
labels.set_width(max_width)
if labels.get_height() > max_height:
labels.set_height(max_height)
if dx_label is not None:
group.dx_label.next_to(group.dx_line,
np.sign(dx) * DOWN,
buff=group.dx_label.get_height() / 2)
group.dx_label.set_color(group.dx_line.get_color())
if df_label is not None:
group.df_label.next_to(group.df_line,
np.sign(dx) * RIGHT,
buff=group.df_label.get_height() / 2)
group.df_label.set_color(group.df_line.get_color())
if include_secant_line:
secant_line_color = secant_line_color or self.default_derivative_color
group.secant_line = Line(p1, p2, color=secant_line_color)
group.secant_line.scale_in_place(secant_line_length /
group.secant_line.get_length())
group.add(group.secant_line)
return group
def organize_matrices(self, left, right, result):
equals = TexMobject("=")
everything = VGroup(left, right, equals, result)
everything.arrange_submobjects()
everything.set_width(FRAME_WIDTH - 1)
self.add(everything)
def __init__(self, tex_list, **kwargs):
mobject = TexMobject(self.curr_tex).shift(start_center)
Animation.__init__(self, mobject, **kwargs)
def matrix_to_mobject(matrix):
return TexMobject(matrix_to_tex_string(matrix))
def get_tex(self, *tex, **kwargs):
tex_mob = TexMobject(*tex)
self.put_at_tip(tex_mob, **kwargs)
return tex_mob
def get_det_text(matrix,
determinant=None,
background_rect=True,
initial_scale_factor=2):
parens = TexMobject(["(", ")"])
parens.scale(initial_scale_factor)
parens.stretch_to_fit_height(matrix.get_height())
l_paren, r_paren = parens.split()
l_paren.next_to(matrix, LEFT, buff=0.1)
r_paren.next_to(matrix, RIGHT, buff=0.1)
det = TextMobject("det")
det.scale(initial_scale_factor)
det.next_to(l_paren, LEFT, buff=0.1)
if background_rect:
det.add_background_rectangle()
det_text = VMobject(det, l_paren, r_paren)
if determinant is not None:
eq = TexMobject("=")
eq.next_to(r_paren, RIGHT, buff=0.1)
result = TexMobject(str(determinant))
result.next_to(eq, RIGHT, buff=0.2)
det_text.add(eq, result)
return det_text